Question

How do you solve `3x + 2y = 8`, `6x + 4y = 16` by graphing and classify the system?

Answer 1

The System of Linear Equations is Consistent as it has at least one solution.

The system has an infinite number of solutions and hence it is also Dependent.

Explanation:

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Rewrite the system of linear equations given in slope-Intercept Form:

`color(red)(3x+2y = 8` Equation.1

`color(red)(6x+4y = 16` Equation.2

Equation.1 in Slope-Intercept Form:

`3x+2y = 8`

Subtract `(-3x)` from both sides:

`2y=-3x+8`

Divide both sides by `2` to obtain

`y=(1/2)*(-3x+8)` Equation.3

Equation.2 in Slope-Intercept Form:

`6x+4y=16`

Subtract `(-6x)` from both sides

`4y=-6x+16`

Divide both sides by `4` to obtain

`y=(1/4)*(-6x+16)` Equation.4

Generate tables of values for both Equation.3 and Equation.4:

If you observe the values for both equations, you can see that values are the same and hence the graphs represent the same line.

The system of linear equations has at least one solution, and hence it is Consistent.

The given system of linear equations has an infinite number of solutions, hence it is also Dependent.

Hope it helps.